Year 4 unit overview * Australian Curriculum: Mathematics

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Year 4 unit overview — Australian Curriculum: Mathematics
Source: Australian Curriculum, Assessment and Reporting Authority (ACARA), Australian Curriculum v3.0: Mathematics for Foundation–10, <www.australiancurriculum.edu.au/Mathematics/Curriculum/F-10>.
School name
Unit title
Duration of unit
Our School
Shapes, area, angles and symmetry in the environment
10 hours
Unit outline
Students investigate mathematics in the environment, focusing on the concepts of shape, area, symmetry and angles.
The concept of 2-D shapes is investigated at the beginning of the unit and the concepts of area, symmetry and angles are investigated through the concept of
shape to build upon the learning experiences.
The Australian Curriculum proficiency strands of Understanding, Fluency, Problem Solving and Reasoning describe how content is explored or developed
throughout the unit.
The big idea of the unit is that we can learn about mathematical concepts through our environment.
Inquiry questions for the unit:
 In what ways can we compare the area of shapes?
 How many different composite shapes can be made from a number of squares and triangles?
 How can we use different arrangements of composite shapes?
 Where is symmetry found in our environment?
 Where are angles found in our environment?
Queensland Studies Authority January 2012
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Identify curriculum
Content descriptions to be taught
Number and Algebra
Measurement and Geometry
Shape
 Compare the areas of regular and
irregular shapes by informal
means (ACMMG087)
 Compare and describe two
dimensional shapes that result
from combining and splitting
common shapes, with and without
the use of digital technologies
(ACMMG088)
Location and transformation
 Create symmetrical patterns,
pictures and shapes with and
without digital
technologies (ACMMG091)
Geometric reasoning
 Compare angles and classify them
as equal to, greater than or less
than a right angle (ACMMG089)
Statistics and Probability
General capabilities and
cross-curriculum priorities
Literacy
 Use appropriate mathematical
language specific to the topic,
discuss mathematical prefixes
relevant to shapes
Numeracy
 Make links to real-life applications
ICT capability
 Use an electronic geoboard to
explore composite shapes
 Use a digital camera to record
combinations
 Use drawing tools to create
diagrams of composite shapes
Critical and creative thinking
 Use thinking skills to complete
group activities and open-ended
tasks
Personal and social capability
 Work together to participate in
mathematical investigations and
learning experiences
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Year 4 unit overview Australian Curriculum: Mathematics
Achievement standard
By the end of Year 4, students choose appropriate strategies for calculations involving multiplication and division. They recognise common equivalent fractions in
familiar contexts and make connections between fraction and decimal notations up to two decimal places. Students solve simple purchasing problems. They
identify unknown quantities in number sentences. They describe number patterns resulting from multiplication. Students compare areas of regular and irregular
shapes using informal units. They solve problems involving time duration. They interpret information contained in maps. Students identify dependent and
independent events. They describe different methods for data collection and representation, and evaluate their effectiveness.
Students use the properties of odd and even numbers. They recall multiplication facts to 10 x 10 and related division facts. Students locate familiar fractions on a
number line. They continue number sequences involving multiples of single digit numbers. Students use scaled instruments to measure temperatures, lengths,
shapes and objects. They convert between units of time. Students create symmetrical shapes and patterns. They classify angles in relation to a right angle.
Students list the probabilities of everyday events. They construct data displays from given or collected data.
Proficiencies
Opportunities to develop proficiencies include:
Understanding
 making connections between representations of numbers
 describing properties of symmetrical shapes
Fluency
 communicating sequences of simple fractions
 creating patterns with shapes
Problem Solving
 formulating, modelling and recording authentic situations involving
operations
 using properties of numbers to continue patterns
Reasoning
 comparing angles
Queensland Studies Authority January 2012
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Relevant prior curriculum
Curriculum working towards
In the Australian Curriculum: Mathematics at Year 2
Measurement and Geometry
Shape
 Describe and draw two-dimensional shapes, with and without digital
technologies.
In the Australian Curriculum: Mathematics at Year 3
Measurement and Geometry
Shape
 Make models of three-dimensional objects and describe key features.
Location and transformation
 Identify symmetry in the environment.
Geometric reasoning
 Identify angles as measures of turn and compare angle sizes in everyday
situations.
In the Australian Curriculum: Mathematics at Year 5
Measurement and Geometry
Using units of measurement
 Choose appropriate units of measurement for length, area, volume,
capacity and mass.
 Calculate the perimeter and area of rectangles using familiar metric units.
Shape
 Connect three-dimensional objects with their nets and other twodimensional representations.
Location and transformation
 Describe translations, reflections and rotations of two-dimensional shapes.
Identify line and rotational symmetries.
 Apply the enlargement transformation to familiar two-dimensional shapes
and explore the properties of the resulting image compared with the
original.
Geometric reasoning
 Estimate, measure and compare angles using degrees. Construct angles
using a protractor.
Bridging content
In the Essential Learnings by the end of Year 3, the concept of angles has not been addressed.
Students have previously been taught about simple common fractions and mixed numbers, but the Essential Learnings do not prepare students to count using
these fractions.
Links to other learning areas
Studies of Society and Environment — location and direction, compass points
Visual Art — viewing, discussing and creating symmetrical and asymmetrical pictures and paintings
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Year 4 unit overview Australian Curriculum: Mathematics
Assessment
Make judgments
Describe the assessment
Assessment date
Students are given opportunities to demonstrate their knowledge, skills and
understanding through both formative and summative assessment. The assessment
is collated in student folios and allows for ongoing feedback to students on their
learning.
Year 4 teachers make decisions about the length of time required to complete the
tasks and the conditions under which the assessment is to be conducted.
The teaching and learning experiences throughout the term provide opportunities for
students to develop the understanding and skills required to complete these
assessments. As students engage with these learning experiences the teacher can
provide feedback on specific skills.
Weeks 6–8
Mathematical investigation: Journal (Written)
Investigate shapes, area, angles and symmetry in the environment.
Student journals may include:
 an outline of a composite shape where students have marked in dotted lines to
show at least three different combinations of squares and/or triangles that could
have been used to make the composite shape
 diagrams to show all possible combinations including labels and explanations to
communicate thinking and reasoning and justify
 an annotated picture or photograph of a familiar scene, e.g. classroom or
landscape, that displays understanding and knowledge of the range of concepts
addressed: symmetry, angles, shapes, area. Students may photograph examples
of these concepts within their environment and annotate the photograph/s to
demonstrate understanding.
The assessment package Angles and symmetry in the built environment in the QSA
Assessment Bank could be used in this unit.
Teachers gather evidence to make
judgements about the following
characteristics of student work:
Understanding
 application of mathematical knowledge to
solve problems and to describe and
identify concepts
 description of choices made, strategies
used and conclusions reached, and
checks of the reasonableness of solutions
 modelling and representation
Skills
 application of problem-solving strategies
to investigate situations
 description of the results of mathematical
investigations
 use of mathematical procedures and
calculations to find solutions
 communication of explanations, solutions
and calculations, using mathematical
language, conventions and symbols
For further advice and guidelines on
constructing guides to making judgments
refer to the Learning area standard
descriptors: www.qsa.qld.edu.au
Queensland Studies Authority January 2012
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Teaching and learning
Supportive learning environment
Teaching strategies and learning experiences
Adjustments for needs of learners
Resources
 Ascertain students’ prior knowledge through a class KWL chart about mathematics
in the school environment.
 Create a word wall to record specific mathematical language used in this topic,
which will be added to throughout the learning experiences.
 Use the school environment, including the classroom, to take photos of shapes.
 Use the photos to discuss and revise shape names and properties.
 Discuss the terms “regular” and “irregular” in regard to shapes.
 Discuss prefixes used in shapes, e.g. tri- meaning three, octa- meaning eight.
 Create composite shapes by combining other shapes using attribute or pattern
blocks. Draw an outline of the composite shapes and mark in the component
parts.
 Mark dotted lines on blank shapes to show three or four 2-D shapes within the
shape. Cut along the lines, remake the shape within an outline of the original
shape, then swap parts with a classmate and remake the shape.
 Provide composite shapes partially marked to show component 2-D shapes and
students mark in other shapes.
 Use the outline of a shape, for example a square, and ask students to show
different ways 2-D shapes could have been used to construct the square (e.g.
using only squares, only triangles, squares and triangles).
 Explore tetrominoes and describe the different ways four squares can be
combined to make different shapes.
 Explore the use of symmetry and tessellation in the traditions of other world
cultures, e.g. islamic mosaics.
 Visualise different ways four triangles could be combined and then use materials
to make what has been visualised.
 Use the interactive whiteboard to manipulate shapes to combine and split.
 Locate angles within two-dimensional shapes within the environment. Students
begin by locating right angles and discussing the definition of a right angle. They
then take photos of the environment and select parts of the photo to use to identify
and classify angles as equal to, less than or greater than a right angle.
 Define symmetry through completing a “butterfly print” or finding a picture of a
butterfly. Students make predictions about the definition of symmetry.
Section 6 of the Disability Standards
for Education (The Standards for
Curriculum Development,
Accreditation and Delivery) states
that education providers, including
class teachers, must take
reasonable steps to ensure a
course/program is designed to allow
any student to participate and
experience success in learning.
The Disability Standards for
Education 2005 (Cwlth) is available
from: <www.ag.gov.au> select
Human rights and anti-discrimination
> Disability standards for education.
Equipment
 digital camera/s
 attribute blocks, pattern
blocks, polydrons or
geoshapes
 access to computer drawing
tools
 geoboard
 tangrams
 egg-shaped tangrams
 pentominoes and tetrominoes
Year 4 unit overview Australian Curriculum: Mathematics
Teaching and learning
Supportive learning environment
Teaching strategies and learning experiences
Adjustments for needs of learners
Resources
 Identify objects and living things that display symmetry.
 Create symmetrical patterns, pictures and shapes with and without the use of
digital technologies.
 Relate symmetry to two-dimensional shapes to identify which shapes show
symmetry and draw in the lines of symmetry.
 Discuss the concept of area by investigating ways to compare areas of regular
and irregular shapes using informal means.
 Use a range of regular and irregular shapes to compare areas. These may be
objects within the classroom or within the school environment. Students
investigate and select a range of informal units to compare areas.
Queensland Studies Authority January 2012
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Use feedback
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Ways to monitor learning
and assessment
Teachers meet to collaboratively plan the teaching, learning and assessment to meet the needs of all learners in each unit.
Teachers create opportunities for discussion about levels of achievement to develop shared understandings; co-mark or cross
mark at key points to ensure consistency of judgments; and participate in moderating samples of student work at school or cluster
level to reach consensus and consistency.
Feedback to students
Teachers strategically plan opportunities and ways to provide ongoing feedback (both written and informal) and encouragement to
students on their strengths and areas for improvement.
Students reflect on and discuss with their teachers or peers what they can do well and what they need to improve.
Teachers reflect on and review learning opportunities to incorporate specific learning experiences and provide multiple
opportunities for students to experience, practise and improve.
Reflection on the unit plan
Identify what worked well during and at the end of the unit, including:
 activities that worked well and why
 activities that could be improved and how
 assessment that worked well and why
 assessment that could be improved and how
 common student misconceptions that need, or needed, to be clarified.
Year 4 unit overview Australian Curriculum: Mathematics
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